Every Hilbert space frame has a Naimark complement

Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements with one notable exception. So these complements can be used for equiangular frames, RIP property, fusion frames etc. Along the way, we will correct a mistake in a recent fusion frame paper where chordal distances for Naimark complements are computed incorrectly.Comment: Changes after Refereein

Every Hilbert space frame has a Naimark complement

Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements with one notable exception. So these complements can be used for equiangular frames, RIP property, fusion frames etc. Along the way, we will correct a mistake in a recent fusion frame paper where chordal distances for Naimark complements are computed incorrectly.Comment: Changes after Refereein

Constructing infinite tight frames

Abstract. For finite and infinite dimensional Hilbert spaces H we classify the sequences of positive real numbers {an} ∞ n=1 so that there is a tight frame {ϕn} ∞ n=1 for H satisfying: ‖ϕn ‖ = an, for all n = 1, 2, 3, · · ·. In the finite dimensional case we will identify the frames which are closest to being tight (in the sense of minimizing potential enerty) for any sequence {an} ∞ n=1. 1